Spontaneous curvature of molecular brushes adsorbed on a flat substrate was observed by scanning force microscopy for comblike polymers of poly(butyl acrylate). This phenomenon was analyzed theoretically for a 2D model of a brush molecule in the regime of strong adsorption. Although all side chains were confined to the substrate plane, they were allowed to flip over and change their position with respect to the backbone. Instability of the straight backbone was caused solely by the entropic elasticity of the side chains: smaller extension of the side chains was attained upon their uneven distribution relative to the backbone. An equilibrium, i.e., spontaneous, curvature resulted from competition between elasticity of the side chains and stabilizing factors such as inherent stiffness of the backbone, mixing entropy of the side chains and excluded volume interactions of distant parts of the brush. The curvature radius is found to be proportional to the degree of polymerization of the side chains. The effect of polydispersity of the side chains is discussed.